Divide the following complex numbers. $ \dfrac{-8+12i}{-4i}$
Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{-8+12i}{-4i} = \dfrac{-8}{-4i} + \dfrac{12i}{-4i}$ Factor out a $1/i$ $\dfrac{-8}{-4i} + \dfrac{12i}{-4i} = \dfrac 1i \left( \dfrac{-8}{-4} + \dfrac{12i}{-4} \right) = \dfrac 1i (2-3i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (2-3i) = -i (2-3i) = -2i + 3i^2 = -3-2i$